There appears to be momentum this morning in nuclear talks between Iran and Western countries, led by the United States.

For years, American-led economic sanctions have been meant to squeeze Iran into proving that its nuclear program is for peaceful purposes, not for bombs. But the election of a new Iranian president this summer raised hopes for a new approach: negotiations.

A round of talks began in Geneva this week. And today, Secretary of State John Kerry is going there from the Middle East, apparently to help narrow remaining differences.

Last night, President Obama spoke about the strategy in an interview with NBC.

(SOUNDBITE OF NBC INTERVIEW)

PRESIDENT BARACK OBAMA: So, we don't have to trust them. What we have to do is to make sure that there is a good deal in place from the perspective of us verifying what they're doing, and that they're actually moving in the right direction.

GREENE: NPR's Peter Kenyon has been covering the talks in Geneva, and is on the line with us. Peter, good morning.

PETER KENYON, BYLINE: Morning, David.

GREENE: So, we've been hearing from the Iranians all week, saying that despite all these years of failure, that a deal really could be reached this week. And I wonder if John Kerry's arrival gives some credence to that.

KENYON: No question. It raises the expectations. I mean, there was some surprise when the foreign minister of Iran kept saying, yes, it can be done this round. Was it just a negotiating tactic? But then Mohammad Javad Zarif canceled his trip to Rome yesterday to stay in the talks. And now, with the news that Kerry is adding Geneva to his schedule at the last minute, and we're also hearing that possibly the French foreign minister may arrive in Geneva. So, expectations are really going up quickly that a joint statement that could be crafted today might well outline a first step agreement that contains the first real limits on Iran's nuclear program in nearly a decade. And if that holds, then time would be bought to work out a comprehensive nuclear deal over the next coming months.

GREENE: OK. So we're talking about some limits that Iran might have to agree to on their nuclear program. They want sanctions eased. What details of a potential deal do we know so far?

KENYON: Well, we know that the most immediate concern of the U.S. and its allies is this enrichment of uranium to 20 percent - more than you need for nuclear power, well on the way to weapons grade. That's 90 percent. If Iran agrees to suspend the 20 percent enrichment and reduce its existing stockpile, put it out of reach, that would ease a lot of the fears that Tehran is getting closer and closer to some day producing nuclear weapons fuel. Iran, of course, says it doesn't want or need that.

Another big issue is centrifuges. These are the units that actually spin and enrich the uranium. Experts warn that if there isn't a cap on that in this first phase, then if the final talks break down in the coming months, Iran could emerge closer than ever to having this weapons-grade fuel. So verification is going to be key.

And on the sanctions side, for Iran's part, they're not getting everything they want. We're told they would get limited sanctions relief, and probably some badly needed currency, but the regime of sanctions itself would remain in place.

GREENE: Peter Kenyon, one part of the story that has been very important is that, I mean, this rush of diplomacy has set off major alarm bells with some of America's closest allies in the region. I mean, is Washington managing that, as we might be getting closer here?

KENYON: They're doing their best to manage it with extreme care, David. Before taking off for Geneva, Kerry returned to Israel to meet with Prime Minister Benjamin Netanyahu, who has rejected this deal even before it's announced. He says Washington is on the verge of making a historic mistake. The Saudis are also dismayed at the prospect of warmer ties between Iran and the U.S. That may be why, as we heard, President Obama taking a very cautious approach, downplaying this agreement, not building it up, just talking about a first step in a long process.

GREENE: And, Peter, Iran, I mean, is a key player in the region in crises, like the war in Syria right now. They're close to President Bashar al-Assad's government. If a nuclear agreement actually happens, does that open the door to cooperate with them in other areas?

KENYON: Well, that is the tantalizing prospect analysts are looking at now, and, of course, some very big ifs attached, issues like Syria, Lebanese Hezbollah militia - which Iran supports - might be easier to resolve. History would suggest that if it's possible at all, it's a long way off. But it will be interesting to watch if today's meeting between Secretary Kerry and the other diplomats opens the way for this first small step in that direction.